ARTICLE pubs.acs.org/jced
Excess Molar Enthalpies of Dipropyl Ether þ Dibutyl Ether þ (1-Hexene or Tetrahydrofuran) at 298.15 K S. M. Nazmul Hasan and Ding-Yu Peng* Department of Chemical & Biological Engineering, University of Saskatchewan, Saskatoon, SK S7N 5A9, Canada ABSTRACT: Excess molar enthalpies, measured at the temperature 298.15 K and atmospheric pressure conditions by means of a flow microcalorimeter, are reported for the ternary mixtures {x1 dipropyl ether þ x2 dibutyl ether þ (1 - x1 - x2) (1-hexene or tetrahydrofuran)}. A smooth representation of the results is described and used to construct constant-enthalpy contours on a Roozeboom diagram. It is shown that good estimates of the excess molar enthalpies of the ternary systems can be obtained from the Liebermann-Fried model by using the physical properties of the pure components and the parameters determined from their binary mixtures.
’ INTRODUCTION Addition of oxygenated compounds to gasoline as additives instead of lead has been proposed to reduce the emissions of hazardous compounds, such as carbon monoxide and unburned hydrocarbons. In this connection, ethers are used as oxygenating agents in gasoline blending technology to enhance the octane rating of automotive fuels. In the present study, excess molar enthalpy values for two ternary mixtures at (T = 298.15 K) comprised of dipropyl ether (DNPE), dibutyl ether (DNBE), and {1-hexene (1HX), or tetrahydrofuran (THF)} have been measured. ’ EXPERIMENTAL SECTION The DNPE and 1HX were obtained from Alfa Aesar. The mole fraction purities of these chemicals, as specified by the manufacturer and verified by means of gas chromatography in this laboratory, exceeded 0.990. The DNBE and THF were obtained from Sigma-Aldrich and had a purity of at least 0.999 mol fraction. Apart from degassing, all of the components were used without further purification. Densities, F(T = 298.15 K)/(kg 3 m-3), measured by means of a densimeter (Anton-Paar DMA-5000M), which has a temperature stability of ( 0.001 K and a precision in density measurement of ( 0.001 kg 3 m-3, were (742.00, 763.81, 668.76, and 882.08) kg 3 m-3 for DNPE, DNBE, 1HX, and THF, respectively. These results are in good agreement with the values of (742.59, 763.94, 668.73, and 882.08) kg 3 m-3 for DNPE,1 DNBE,2 1HX2, and THF,3 respectively. A flow microcalorimeter (LKB model-10700-1), thermostatted at 298.150 K, was used to measure the excess molar enthalpies. The temperature of the bath was controlled within ( 0.005 K of the specified temperature. The calorimeter system was essentially the same one that was used in the previous work1-7 except for a modified flow measuring system. The modification involved replacing the old direct current motors and controllers with two new stepper motors and digital speed controllers. Each of the transparent disks with 120 equally spaced radial photomasked sectors for optical sensor was also replaced by a similar r 2010 American Chemical Society
disk with 180 sectors. This replacement has increased the counts per revolution of the motor from 120 to 180; the precision of the flow rate readings has thus been improved by about 50 %. Details of the equipment and the operating procedure have been described previously.6,7 In studying the ternary systems {x1 DNPE þ x2 DNBE þ (1 - x1 - x2) (1HX or THF)}, the excess molar enthalpies HEm,1þ23 were determined for several pseudobinary mixtures. The ternary mixtures were formed by adding component 1 (DNPE) to binary mixtures of fixed composition of component 2 (DNBE) and component 3 (1HX or THF). The fixed-composition binary mixtures with selected values of x2/(1 - x1 - x2) were prepared by weighing. The excess molar enthalpy HEm,123 for the ternary mixture was then obtained from the relation E E E ¼ Hm;1þ23 þð1 - x1 ÞHm;23 Hm;123
ð1Þ
where HEm,23 is the excess molar enthalpy of the particular binary mixture. Over most of the composition range, the errors of the excess molar enthalpies and those of the mole fractions of the final ternary mixtures are estimated to be less than 0.005 3 |HEm| and less than 5 3 10-4, respectively.
’ RESULTS AND DISCUSSION Excess molar enthalpies, HEm,ij (i < j), for one of the five constituent binary mixtures of the present interest, have been reported previously: {DNBE (2) þ 1HX (3)}.3 In the course of the present investigation, the experimental excess molar enthalpy values for the other four binary mixtures {DNPE (1) þ DNBE (2) or 1HX (2) or THF (2)} and {DNBE (2) þ THF (3)} at T = 298.15 K have been measured and are summarized in Table 1. Special Issue: John M. Prausnitz Festschrift Received: August 31, 2010 Accepted: October 14, 2010 Published: November 02, 2010 946
dx.doi.org/10.1021/je100897y | J. Chem. Eng. Data 2011, 56, 946–950
Journal of Chemical & Engineering Data
ARTICLE
Table 1. Experimental Mole Fraction xi and Excess Molar Enthalpies HEm,ij at 298.15 K, for {x1 þ (1 - x1) DNBE}, {x1 DNPE þ (1 - x1) 1HX}, {x1 DNPE þ (1 - x1) THF}, and {x1 DNBE þ (1 - x1) THF}a HEm,ij xi
HEm,ij
J 3 mol-1
xi
HEm,ij
J 3 mol-1
HEm,ij
J 3 mol-1
xi
J 3 mol-1
xi
DNPE (i) þ DNBE (j) 0.0500
2.23 0.3000
9.57 0.5004
11.85 0.7500
9.55
0.1000
4.27 0.3500
10.31 0.5500
11.88 0.8000
8.18
0.1500
5.86 0.3998
10.94 0.6001
11.76 0.8503
6.66
0.2001
7.32 0.4497
11.52 0.6500
11.32 0.9000
4.63
0.2500
8.56 0.4998
11.85 0.6999
10.57 0.9500
2.56
0.0529
6.60 0.3002
24.91 0.5001
28.00 0.7500
21.54
0.1001 0.1500
12.08 0.3499 16.49 0.4001
26.45 0.5500 27.35 0.5998
27.65 0.8003 26.83 0.8500
18.83 15.38
0.2001
20.10 0.4501
28.09 0.6499
25.48 0.9000
11.33
0.2500
22.82 0.5001
28.00 0.6996
23.85 0.9500
6.10
0.0500
52.28 0.2998
216.9
0.4998
248.6
0.7499
184.5
0.1000
96.88 0.3503
232.8
0.5499
244.6
0.7999
159.4 127.7
DNPE (i) þ 1HX (j)
Figure 1. Excess molar enthalpies, HEm,ij/(J 3 mol-1), for binary systems presented in Table 1 at the temperature 298.15 K. Experimental results: Δ, {x1 DNPE þ (1 - x1) DNBE}; !, {x1 DNPE þ (1 - x1) 1HX}; ., {x1 DNPE þ (1 - x1) THF}; 3, {x1 DNBE þ (1 - x1) THF}. Curves: blue —, calculated from the representations of the results by eq 2 with values of the coefficient given in Table 2; red - - -, fit of results by the Liebermann-Fried model.
DNPE (i) þ THF(j)
0.1501
136.1
0.3998
242.6
0.5999
236.3
0.8500
0.2000 0.2498
168.2 195.9
0.4500 0.4998
247.3 248.3
0.6502 0.7003
223.7 206.2
0.9000 0.9500
also included in Table 2. The experimental results and their representations by eq 2 for the four binary mixtures investigated in this study are plotted in Figure 1. It is seen that for all four binary mixtures the maximum values of HEm,ij occur near x1 ≈ 0.50, and the curves are nearly symmetric about that point. The experimental results for the ternary mixtures are reported in Tables 3 and 4, where values of HEm,1þ23 are listed against the mole fraction x1 of DNPE. Also included in the table are the corresponding values of HEm,123 calculated from eq 1. The values of HEm,1þ23 are plotted in Figures 2 and 3, along with curves for the constituent binary mixtures having x3 = 0.0 and x2 = 0.0. In all cases, the maximum values of HEm,1þ23 and HEm,123 occur near x1 ≈ 0.50. Representation of the values of HEm,1þ23 is based on the relation8 x2 x3 E E E Hm;1þ23 ¼ ð3Þ Hm;12 þ H E þ Hm;T 1 - x1 1 - x1 m;13
90.47 48.08
DNBE (i) þ THF(j) 0.0500
a
78.75 0.3000
305.8
0.4998
339.3
0.7501
240.4
0.0998
143.6
0.3499
324.9
0.5498
331.9
0.8000
204.1
0.1502
198.4
0.4000
336.8
0.6002
318.2
0.8500
162.2
0.2000
243.4
0.4502
341.5
0.6499
297.9
0.9000
112.1
0.2500
278.7
0.4998
339.0
0.7000
272.7
0.9500
59.48
Where i < j.
Table 2. Coefficients hk and Standard Deviations s for the Representations of the Excess Molar Enthalpies HEm,ij of the Constituent Binary Mixtures at 298.15 K by Equation 2 s
component i
j
DNPE DNBE
h2
47.28 -7.34
h3
h4
h5
J 3 mol-1
3.61
6.59
DNPE 1HX 111.98 7.48 26.22 1HX DNBE -96.39 -4.16 -8.74
-3.83
0.10 0.20a
91.65 -36.23 -23.01
0.43
DNPE THF DNBE THF a
h1
993.78
66.65
1358.73 192.51 108.67
34.27
which consists of the sum of the binary contributions and an added ternary term HEm,T. The ternary term is given by
0.06
E Hm;T =ðJ 3 mol-1 Þ ¼ x1 x2
0.49
Wang et al.2
1 - x1 - x2 ðc0 þ c1 x1 þ c2 x2 þ c3 x21 1 - x1 þ x2
þ c4 x1 x2 þ c5 x22 þ ... Þ
The smoothing function E Hm;ij =ðJ 3 mol-1 Þ ¼ xi ð1 - xi Þ
n
∑ hk ð1 - 2xi Þk - 1 k¼1
ð4Þ
and is similar to that used by Morris et al.9 with an extra skewing factor (1 - x1 þ x2)-1 inserted.1,2,4,5 Values of the coefficients ci were obtained from least-squares analyses in which eqs 3 and 4 were fitted to the experimental values in Tables 3 and 4. In doing this, the values of HEm,ij for the binary contributions were calculated from eq 2 using appropriate coefficients from Table 2. The resulting representations of HEm,T are given in the footnote of Tables 3 and 4, along with the standard deviations s of
ð2Þ
was fitted to these experimental values by the method of unweighted least-squares. The results of the data correlation for the binary systems are summarized in Table 2, along with the standard deviations of the representations. For convenience, the coefficients for the {DNBE (2) þ 1HX (3)}3 binary mixture are 947
dx.doi.org/10.1021/je100897y |J. Chem. Eng. Data 2011, 56, 946–950
Journal of Chemical & Engineering Data
ARTICLE
Table 3. Experimental Excess Molar Enthalpies HEm,1þ23 at the Temperature 298.15 K for the Addition of DNPE to DNBE and 1HX to Form {x1 DNPE þ x2 DNBE þ (1 - x1 x2) 1HX} and Values of HEm,123 Calculated from Equation 1 Using HEm,23 Obtained from Equation 2 with Coefficients from Table 2a
x1
HEm,1þ23
HEm,123
HEm,1þ23
J 3 mol-1
J 3 mol-1 x1
J 3 mol-1
HEm,123 J 3 mol-1 x1
HEm,1þ23
HEm,123
J 3 mol-1
J 3 mol-1
Table 4. Experimental Excess Molar Enthalpies HEm,1þ23 at the Temperature 298.15 K for the Addition of DNPE to DNBE and THF to Form {x1 DNPE þ x2 DNBE þ (1 - x1 x2) THF} and Values of HEm,123 Calculated from Equation 1 Using HEm,23 Obtained from Equation 2 with Coefficients from Table 2a E Hm,1þ23
x1
J 3 mol-1
HEm,123
HEm,1þ23
J 3 mol-1 x1
HEm,123
J 3 mol-1
J 3 mol-1 x1
HEm,1þ23
HEm,123
J 3 mol-1
J 3 mol-1
x2/x3 = 0.3333, HEm,23/(J 3 mol-1) = 278.67
x2/x3 = 0.3333, HEm,23/(J 3 mol-1) = -18.87
0.0500
5.17
-12.77 0.4001 25.56
14.24 0.7003 23.37
17.71
0.1000
9.58
-7.40 0.4496 26.42
16.03 0.7500 21.38
16.66
0.1500 13.58
-2.46 0.5002 26.74
17.30 0.7998 18.98
15.20
0.1998 17.00
1.89 0.5002 26.76
17.33 0.8500 15.79
12.96
0.2501 20.03
5.87 0.5503 26.63
18.14 0.9000 12.19
10.30
0.3001 22.34
9.13 0.5999 26.01
18.46 0.9500
0.3501 24.31
12.05 0.6501 24.91
7.12
6.18
18.31
0.0500 21.23
285.9 0.4002 104.2
271.3 0.7016 91.32
174.5
0.1000 38.77
289.6 0.4497 106.8
260.2 0.7501 82.75
152.4
0.1500 55.28
292.2 0.5001 108.1
247.4 0.8000 70.77
126.5
0.2002 69.21
292.1 0.5001 108.1
247.4 0.8500 58.22
100.0
0.2502 80.89
289.9 0.5501 107.2
232.6 0.9001 42.52
70.37
0.3000 90.83
285.9 0.5999 104.6
216.1 0.9500 24.11
38.05
0.3499 98.35
279.5 0.6503
196.4
98.89
x2/x3 = 1.0004, HEm,23/(J 3 mol-1) = 339.67
x2/x3 = 0.9996, HEm,23/(J 3 mol-1) = -24.10
0.0500
4.31
-18.59 0.4001 22.65
8.20 0.7001 21.29
14.06
0.1000
8.18
-13.51 0.4502 23.40
10.15 0.7499 19.61
13.58
0.1499 11.67
-8.82 0.5000 23.87
11.83 0.8001 17.29
12.48
0.2001 14.73
-4.54 0.5000 23.92
11.87 0.8500 14.71
11.09
0.2499 17.33
-0.75 0.5500 23.94
13.10 0.9000 11.65
9.24
0.2999 19.50
2.63 0.6003 23.52
13.89 0.9500
6.60
0.3502 21.17
5.51 0.6500 22.51
14.08
7.81
0.0500
6.53
329.2 0.4002
35.13
238.9 0.7000 33.19
135.1
0.1000 12.61
318.3 0.4502
36.49
223.2 0.7498 30.26
115.2
0.1500 17.85
306.6 0.5002
37.33
207.1 0.8001 26.65
94.56
0.2000 22.78
294.5 0.5001
37.29
207.1 0.8500 21.86
72.81
0.2503 27.02
281.7 0.5501
37.25
190.1 0.9000 15.93
49.89
0.3002 30.21
267.9 0.5998
36.64
172.6 0.9500
8.69
25.67
0.3499 32.90
253.7 0.6500
35.14
154.0
x2/x3 = 3.0000, HEm,23/(J 3 mol-1) = 241.00
x2/x3 = 3.0000, HEm,23/(J 3 mol-1) = -18.10
0.0500
3.03
-14.16 0.4000 16.89
6.04 0.6997 16.76
11.33
0.1000
5.83
-10.46 0.4501 17.62
7.67 0.7497 15.43
10.90
0.1500
8.45
-6.93 0.4996 18.12
9.06 0.7998 13.94
10.31
0.1999 10.66
-3.82 0.4997 18.16
9.11 0.8497 12.06
9.34
0.2501 12.75
-0.82 0.5497 18.28
10.13 0.9000
9.72
7.92
0.3001 14.43
1.77 0.6001 18.08
10.84 0.9500
6.39
5.48
0.3499 15.85
4.09 0.6497 17.51
11.17
1.93
230.9 0.4002
8.50
153.1 0.7001
7.80
80.09
0.1000
3.52
220.4 0.4503
8.80
141.3 0.7498
7.11
67.40
0.1555
5.01
208.5 0.5001
8.91
129.4 0.8000
6.25
54.45
0.2000
5.95
198.8 0.5001
8.91
129.4 0.8500
5.13
41.29
0.2498
6.89
187.7 0.5501
8.89
117.3 0.9000
3.75
27.86
0.2999
7.55
176.3 0.6000
8.68
105.1 0.9500
2.03
14.07
0.3502
8.16
164.8 0.6501
8.35
92.68
a
Ternary term for representation of HEm,1þ23 by eqs 3 and 4: Hm, -1 T /(J 3 mol ) = [x1x2x3/(1 - x1 þ x2)](-2979.96 þ 2782.56x1þ 675.29x2 - 1947.11x21 - 2677.41x1x2); s/(J 3 mol-1) = 0.69.
a
Ternary term for representation of HEm,1þ23 by eqs 3 and 4: Hm, E -1 T /(J 3 mol ) = [x1x2x3/(1 - x1 þ x2)] (-251.11 þ 1270.01x1 þ 699.74x2 - 2238.89x21 - 428.01x1x2 - 798.02x22 þ 1557.48x31); s/(J 3 mol-1) = 0.43.
the fit. The solid curves for HEm,1þ23 in Figures 2 and 3 were calculated from eq 3. Equations 1 to 4 were also used to calculate the constant HEm,123 contours plotted on the Roozeboom diagram in Figures 4(a) and 5(a). For the {DNPE (1) þ DNBE (2) þ 1HX (3)} ternary system, Figure 4(a) serves to show that there exists an internal saddle point. However, the point representing the maximum value of HEm,123 (28.4 J 3 mol-1) is located on the DNPE-1HX edge. For the {DNPE (1) þ DNBE (2) þ THF (3)} ternary system, Figure 5(a) serves to show that there is no internal extremum; the point representing the maximum value (341.52 J 3 mol-1) is located on the DNBE-THF edge. Wang et al.5 have shown that the Liebermann-Fried model10,11 can be used to represent the excess molar enthalpies for both binary and multicomponent mixtures. For representing the excess molar enthalpy of a multicomponent mixture, only the properties of the pure components and interaction parameters derived from the analyses of the excess enthalpies of the constituent binaries are required. Details of the thermodynamic relations in connection with the derivation and application of the Liebermann-Fried model were described by Peng et al.12 A brief
0.0500
E
discussion of the Liebermann-Fried model is presented below to facilitate our understanding of this model. According to the Liebermann-Fried model, the excess molar enthalpy of an N-component mixture is represented by the equation H E ¼ HðIÞ þ HðV Þ
ð5Þ
where N
HðIÞ ¼ ðRT 2 =2Þ 2
N
∑ ∑ xj xk j¼1 k¼1
8 N > > > >
Akj > 6 > > 6 : 6 6 ! N 6 6 xp Ajp 4
∑
p¼1
∑
N
∑ xp Ajp
p¼1 N
∑ xqAkq
q¼1
!
93 > > >7 7 xq ðDAkq =DTÞ> = q¼1 7 þ 7 N >7 > > > xq Akq ;7 7 q¼1 7 7 7 7 5 N
∑
∑
ð6Þ 1 DAjk ¼ Ajk DT 948
lnðAjk Akj Þ β 1 DAkj ¼ T lnðAjk Akj Þ - 2 Akj DT
ð7Þ
dx.doi.org/10.1021/je100897y |J. Chem. Eng. Data 2011, 56, 946–950
Journal of Chemical & Engineering Data
ARTICLE
Figure 2. Excess molar enthalpies, HEm,1þ23/(J 3 mol-1), for {x1 DNPE þ x2 DNBE þ (1 - x1 - x2) 1HX} mixtures at the temperature 298.15 K. Plotted against mole fraction x1. Experimental results: Δ, x3 = 0.0; ., x2/x3 = 0.3333; 9, x2/x3 = 0.9996; ~, x2/x3 = 3.0000; 3, x2 = 0.0. Curves: blue —, calculated from the representation of the results by eqs 3 and 4 using the ternary term HEm,T given in the footnote of Table 3; red ---, estimated by means of the Liebermann-Fried model.
Figure 4. Contours for constant values of HEm,123/(J 3 mol-1) for {x1 DNPE þ x2 DNBE þ (1 - x1 - x2) 1HX} at 298.15 K. Part (a) calculated from the representation of the experimental results by eqs 3 and 4, with HEm,T from the footnote of Table 3. Part (b) estimated by means of the Liebermann-Fried model.
The term H(I) accounts for the nonideal behavior arising from the interaction between molecules, whereas the term H(V) accounts for the effect of the different sizes (i.e., molar volume) of the molecules in the mixture. The symbols vk and (RP)k in eq 8 represent, respectively, the molar volume and the isobaric thermal expansivity of pure component k. The values of the interaction parameters Aij and Aji determined for the constituent binaries are given in Table 5. These parameters were obtained by fitting the Liebermann-Fried formula for HEm,ij to the experimental results for the excess molar enthalpies given in Table 1. Also included in that table are values of the standard deviations s and values of the isobaric thermal expansivities.13 The Liebermann-Fried model has the potential to represent vapor-liquid equilibria of systems containing hydrocarbons and ethers using the pure component properties (i.e., isobaric thermal expansivities) and the binary parameters obtained by fitting the excess molar enthalpy data.12,13
Figure 3. Excess molar enthalpies, HEm,1þ23/(J 3 mol-1), for {x1 DNPE þ x2 DNBE þ (1 - x1 - x2) THF} mixtures at the temperature 298.15 K. Plotted against mole fraction x1. Experimental results: Δ, x3 = 0.0; ., x2/x3 = 0.3333; 9, x2/x3 = 1.0004; ~, x2/x3 = 3.0000; 3, x2 = 0.0. Curves: blue —, calculated from the representation of the results by eqs 3 and 4 using the ternary term HEm,T given in the footnote of Table 4; red ---, estimated by means of the Liebermann-Fried model.
and N
HðV Þ ¼ ðRT 2 Þ
N
∑ ∑ xj xkυk ½ðRP Þk - ðRP Þj j¼1 k¼1 N
∑ xk υk
ð8Þ
k¼1
949
dx.doi.org/10.1021/je100897y |J. Chem. Eng. Data 2011, 56, 946–950
Journal of Chemical & Engineering Data
ARTICLE
cases, it can be seen that the theory predicts correctly the order of the three experimental curves and their positions relative to the curves for the two constituent binaries. The root-mean-square deviations of the values presented in Tables 3 and 4, each with 60 data points, are 1.59 J 3 mol-1 and 6.0 J 3 mol-1. Constant HEm,123 contours, estimated on the basis of the Liebermann-Fried model, are shown on the Roozeboom diagram in Figures 4(b) and 5(b). It is clear from a comparison of the two parts in each figure that the Liebermann-Fried model provides useful estimation of HEm,123 for both the present mixtures, including predictions of the locations and magnitudes of the external maxima.
’ AUTHOR INFORMATION Corresponding Author
*Tel.: þ1-306-966-4767. Fax: þ1-306-966-4777. E-mail address: [email protected]. Funding Sources
The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged.
’ REFERENCES (1) Liao, D. K.; Tong, Z. F.; Benson, G. C.; Lu, B. C.-Y. Excess Enthalpies of (n-C7 or n-C10) þ MTBE þ DNPE Ternary Mixtures at 298.15 K. Fluid Phase Equilib. 1997, 131, 133–143. (2) Wang, Z.; Benson, G. C.; Lu, B. C.-Y. Excess Enthalpies of Binary Mixtures of 1-Hexene with Some Ethers at 25 °C. J. Solution Chem. 2004, 33, 143–147. (3) Lan, Q. C.; Kodama, D.; Wang, Z.; Lu, B. C.-Y. Excess Molar Enthalpies of Mixtures (1-Hexene þ Tetrahydrofuran or 2-Methyltetrahydrofuran þ Methyl tert-butyl ether) at the Temperature 298.15 K. J. Chem. Thermodyn. 2006, 38, 1606–1611. (4) Peng, D.-Y.; Benson, G. C.; Lu, B. C.-Y. Excess Enthalpies of Heptane þ Ethanol þ 1,2-Dimethoxyethane at 298.15 K. J. Chem. Eng. Data 1998, 45, 880–883. (5) Wang, Z.; Peng, D.-Y.; Benson, G. C.; Lu, B. C.-Y. Excess Enthalpies of (Ethyl tert-butylether þ Hexane þ Heptanes, or Octane) at the Temperature 298.15 K. J. Chem. Thermodyn. 2001, 33, 1181–1191. (6) Tanaka, R.; D’Arcy, P. J.; Benson, G. C. Application of a Flow Microcalorimeter to Determine the Excess Enthalpies of Binary Mixtures of Non-electrolytes. Thermochim. Acta 1975, 11, 163–175. (7) Kimura, F.; Benson, G. C.; Halpin, C. J. Excess Enthalpies of Binary Mixture of n-Heptane with Hexane Isomers. Fluid Phase Equilib. 1983, 11, 245–250. (8) Tsao, C. C.; Smith, J. M. Heats of Mixing of Liquids. Chem. Eng. Prog. Symp. Ser. 1953, No. 7 (49), 107–117. (9) Morris, J. W.; Mulvey, P. J.; Abbott, M. M.; Van Ness, H. C. Excess Thermodynamic Functions for Ternay Systems. I. Acetone Chloroform-Methanol at 50 °C. J. Chem. Eng. Data, 1975, 20, 403–405. (10) Liebermann, E.; Fried, V. Estimation of the Excess Gibbs Free Energy and Enthalpy of Mixing of Binary Nonassociated Mixtures. Ind. Eng. Chem. Fundam. 1972, 11, 350–354. (11) Liebermann, E.; Fried, V. The Temperature Dependence of Excess Gibbs Free Energy of Binary Nonassociated Mixtures. Ind. Eng. Chem. Fundam. 1972, 11, 354–355. (12) Peng, D.-Y.; Wang, Z.; Benson, G. C.; Lu, B. C.-Y. Predicting the Excess Enthalpies and Vapor-Liquid Equilibria of Multicomponent Systems Containing Ether and Hydrocarbons. Fluid Phase Equilib. 2001, 182, 217–227. (13) Wang, Z.; Lu, B. C.-Y.; Peng, D.-Y.; Lan, C. Q. LiebermannFried Model Parameters for Calculating Vapour-Liquid Equilibria of Oxygenate and Hydrocarbon Mixture. J. Chin. Inst. Eng. 2005, 28, 1089–1105.
Figure 5. Contours for constant values of HEm,123/(J 3 mol-1) for {x1 DNPE þ x2 DNBE þ (1 - x1 - x2) THF} at 298.15 K. Part (a) calculated from the representation of the experimental results by eqs 3 and 4, with HEm,T from the footnote of Table 4. Part (b) estimated by means of the Liebermann-Fried model.
Table 5. Values of the Interaction Parameters Aij and Aji, Standard Deviation s, and Isobaric Thermal Expansivities rp at 298.15 K Used in the Liebermann-Fried Model Calculation
i
a
j
Rp/kK-1
s
component Aij
Aji
J 3 mol-1
i
j b
1.126b 1.411b
DNPE DNPE
DNBE 1HX
1.1072 0.9329
0.8908 1.0455
0.15 0.86
1.261 1.261
1HX
DNBE
0.9354a
1.0759a
0.59
1.411
1.126
DNPE
THF
0.8743
0.9575
2.38
1.261
1.138b
DNBE
THF
0.7579
1.0287
2.41
1.126
1.138
Wang et al.2 b Wang et al.13
Estimates of HEm,1þ23, derived from the Liebermann-Fried model, are shown as dashed curves in Figures 2 and 3. In both 950
dx.doi.org/10.1021/je100897y |J. Chem. Eng. Data 2011, 56, 946–950
